An
Aside: Jell-o and Human Thought.So how bad are Frank's theories? Actually, they're pretty good.
They may not be true, but they are testable, meaningful theories.
In this, they are superior to most of the theories proposed by
humans. Many propositions forwarded by the Human species are so
vague, so amorphous that it's hard to see what they really mean.
To a scientist, meaning IS testability. Every theory must contain
the possibilty of being proven false.
But many human theories don't meet even this test. They avoid
disconfirmation by being free of content, and often survive through
their vapidity. They are the Jell-o of human thought.
An
Aside: Jell-o and Human Thought.
An
Aside: Testability and Falsifiability.... in a bit more detail.
What about Frank's theories? Could a scientist take them seriously, and test them? For fun, let's take a closer look.
Frank surmises that the Sun is a giant Carrot seen from one
end. One might, as a human, scoff at such a silly idea, but this
is unfair. Carrots hold a place of high esteem for Frank; in his
attempt to unify the universe, he associates one great life-force
(The Sun) with another (the Carrot). Taken literally, it is also
a scientific theory; it is meaningful and testable (at least in
principle).
Is it not possible that Frank is correct? Can
you prove him wrong?
There are two aspects to the theory that the sun is a carrot;
there is the question of shape, and that of substance.
In other words, is the sun shaped like a carrot, and is it made
of carrot material?
A carrot is roughly conical, and if it presented the round end
towards the earth, it would seem like a disc, which is the way
it seems to us. It may be a little less orange than most carrots,
but I've seen a few carrots that were close to sun-yellow.
Even a Scientific Frank would have no rocket ship, so he could
not examine the sun from the side. A less contented Frank might
travel a few hundred miles and see if that changed the way the
sun looked. If it stayed the same shape, that could count as a
disconfirmation. (Note -- the ancient Greeks learned a lot about
the universe by comparing times and observations from distant
cities. Not Plato, of course... other ancient Greeks).
A more serious difficulty is the question of substance. Even Frank
must have noticed that the sun gives off a lot of light and warmth.
Generally speaking, carrots do not. Of course, the sun might be
a burning carrot, and an experimentally-minded Frank might have
tried to set fire to a carrot; if so, he would find that it burns
up fairly quickly if he managed to light it at all. This would
count as a pretty serious dis-confirmation.
But let's not be too hard on Frank! Until the 1920's NO theory
of the sun could explain its output of energy! In other words,
from the dawn of human history, till a mere 90 years ago, Franks
theory of the sun was just as good as any theory that had been
thought up by humans!
(Einstein's theory of relativity explained the problem, but heck,
Frank's no Einstein. If he had been, he might have surmised that
it was a radioactive carrot!)
For
more on the history of Astronomy....
So what should Frank do with this unlikely but still not totally
impossible theory? Believe it or reject it? Now, there are some
who feel that all propositions must be either believed OR reviled.
However, a scientific thinker will understand that almost everything
is more or less uncertain, and that little, if anything, reaches
total confirmation or disconfirmation. (Though a lot of things
come damn close).
So Frank doesn't have to make a choice right away. He can wait
for more evidence to come in. I think Frank's most sensible alternative
would be to place this theory in the category of highly-unlikely-but-we-can-always-dust-it-off-again-if-new-evidence-comes-to-light.
If someone asks him what the sun is made of, the correct answer
is, "I don't know. Probably not carrot."
An
Aside: A less literal interpretation of Frank's Sun-Carrot Identity.
Frank surmises that the length of a carrot, divided by its diameter, is always an integer. What does Frank mean by this? The proposition (perhaps described symbolically as lc/dc=I) does have simplicity and beauty; properties highly prized in scientific theories. But the theory has more of the flavour of a Euclidean theorem than a scientific theory; for one thing integers don't turn up in the real universe with quite the frequency that they do in the geometrical one.
The world is too fuzzy. Quantum effects alone would make such an exact result unlikely. Of course, in the case of carrots, we don't have to go to a sub-microscopic level to find fuzziness. It's not that clear where to start measuring the beginning and end of a carrot.
One might assume that Frank simply liked the sound of the theory;
he was pleased with the aesthetic. Unchallenged by criticism from
his peers...he has none...he neither thought about it too deeply,
nor tested it.
Now, we could dismiss the theory as meaningless, but that would
be unfair. With a little spit and polish we can turn this theory
into a testable and plausible one; in fact, a theory which would
please both Platonists and scientists alike.
Imagine that there is an Ideal Carrot (somewhere in Platonic Ideal
Space) which has a ratio of length to diameter equal to "Ideal
Integer". This Carrot casts shadows which are the sub-ideals;
that is to say individual (but still ideal) carrots with proportions
of 1,2,3 etc....
Now these sub-ideals cast shadows into our own universe; we perceive
them as the actual carrots around us. Shadows can be fuzzy, and
so real carrots may only approximate integers.
Is this theory testable? Sure, as long as we don't make the shadows
TOO fuzzy....imagine that we measured, say, a million carrots,
and plotted the results of our test... if there turned out to
be peaks that were fairly near to integer values, then we'd have
a plausible theory.
I'll leave it to the reader to actually perform this experiment.
I measured about twenty-five carrots (two bags!) and the results
were inconclusive. You'd need to measure at least a few thousand
to get an idea of where the experiment was going.
Strangely enough, there is a branch of science in which a rather
similar theory works well! If you plot the harmonics that are
created by plucking a stretched string, or blowing through a pipe,
you'll find they form a series of integers, give-or-take a bit
of physical-universe fuzziness! We now know quite a bit about
why this works... ...and
it doesn't have much to do with Platonic Ideals; but it's no wonder
that the study of musical harmonics was so loved by the ancients,
Plato included.
Once again, Frank isn't totally out to lunch. He's got a knack
for a good theory. He just falls down a bit when it comes to actually
measuring the carrots.